A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n1 = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location. x1: Region I Data 1 7 7 6 5 8 8 1 3 3 3 2 5 1 4 6 A second random sample of n2 = 15 locations in region II gave the following information about the number of cases of fox rabies near that location. x2: Region II Data 3 2 1 4 2 8 5 4 4 4 2 2 5 6 9 Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.Use a calculator with sample mean and sample standard deviation keys to find x1 and s1 in region I, and x2 and s2 in region II. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.) (i) What is the level of significance? (b) What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)(iii) Find the P-value. (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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A study of fox rabies in southern Germany gave the following information about different regions and the occurrence of rabies in each region. A random sample of n₁ = 16 locations in region 1 gave the following information about the number of cases of fox rabies near that location.

x₁: Region I Data

1	7	7	6	5	8	8	1
3	3	3	2	5	1	4	6

A second random sample of n₂ = 15 locations in region II gave the following information about the number of cases of fox rabies near that location.

x₂: Region II Data

3	2	1	4	2	8	5	4
4	4	2	2	5	6	9

Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Use a calculator with sample mean and sample standard deviation keys to find

x₁

and s₁ in region I, and

x₂

and s₂ in region II. (Round your answers to two decimal places.)

x₁	=
s₁	=
x₂	=
s₂	=

(a) Does this information indicate that there is a difference (either way) in the mean number of cases of fox rabies between the two regions? Use a 5% level of significance. (Assume the distribution of rabies cases in both regions is mound-shaped and approximately normal.)

(i) What is the level of significance?

(b) What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

(iii) Find the P-value. (Round your answer to four decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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